You probably made a mistake with the calculation of the period. The amplitude of this graph and $\displaystyle{y}={2}{\sin{{3}}}{x}\usepackage{cmbright}\Huge\$ is 2. However, this graph has half a cycle in the interval $\displaystyle{\left[{0},{3}\pi\right]}\usepackage{cmbright}\Huge\$ , so it has a period of $\displaystyle{6}\pi\usepackage{cmbright}\Huge\$ . But $\displaystyle{y}={2}{\sin{{3}}}{x}\usepackage{cmbright}\Huge\$ has a period of $\displaystyle\frac{{{2}\pi}}{{3}}\usepackage{cmbright}\Huge\$ .